C₅×#64520 #13095054

order	1520
isoclinism	isoclinic class of Dic₃₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

metacyclic
supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₅×#64520

Splittings

Hall	C₅×C₁₉ ⋊ M₁₆
Sylow	C₁₉ ⋊ C₅×M₁₆

Subgroups

	subgroup	G/H
center	C₄×C₅	C₂×D₁₉
commutator	C₂×C₁₉	C₂×C₄×C₅
Frattini	C₄	C₂×C₅×D₁₉
Fitting	C₂×C₄×C₅×C₁₉	C₂
socle	C₂×C₅×C₁₉	C₂×C₄
prime radical	C₂²×C₅×C₁₉	C₄
cosocle	C₄×C₁₉	C₂²×C₅
hypercenter	C₂×C₄×C₅	D₁₉
hypocenter	C₁₉	C₅×M₁₆
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₄×C₅

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 760

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,9,11,13,15,17,19,21,23,24,22,20,18,16,14,12,10,8)(26,29)(30,32);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26,27,30,28,29,31,32)

Conjugacy classes & character table

410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1520, 38);

C5×#64520 #13095054